How do the previously mentioned schools or methods fit into one another? Is nominalism a type of pragmatism? Is pragmatism always a form of empiricism etc.
Pragmatism, Empiricism and Nominalism are different positions, that are each best understood as responding to quite different kinds of questions.
- Nominalism is a metaphysical view about what kinds of things exist. According to nominalists the only things that exist are particular individuals, like Socrates. On this view although we can talk about abstract, universal ideas like "humanity" it is really only particular humans, for instance, that exist.
- Empiricism is an epistemological view about how we know things. Specifically empiricists believe that all of our knowledge is acquired through sensation.
- Although this is somewhat controversial, I think it's best to understand pragmatism as a view about truth. Namely, a pragmatist is a person who believes a sentence is true if and only if it is what we would all agree to, at the ultimate end of inquiry. That is, the truths are the things we'll believe when all the evidence is in, as it were.
Now how are these three positions related? Well, to my knowledge every single pragmatist is also an empiricist, although the converse doesn't hold. Nominalists tend to be empiricists and vice versa, because one of the reasons to be suspicious of universals, as nominalists are, is that it's hard to make sense of how we could ever come to know them, given that we don't experience them. Pragmatists, I would suppose, would tend to be nominalists too, since they're all empiricists, but I wouldn't be surprised if some pragmatists denied nominalism. (All you have to think is that all the evidence isn't in yet about whether we need numbers to be real for science to work, for instance.)
Actually, James makes the connection between pragmatism and nominalism himself. He says in the second chapter:
THEORIES THUS BECOME INSTRUMENTS, NOT ANSWERS TO ENIGMAS, IN WHICH WE CAN REST. We don't lie back upon them, we move forward, and, on occasion, make nature over again by their aid. Pragmatism unstiffens all our theories, limbers them up and sets each one at work. Being nothing essentially new, it harmonizes with many ancient philosophic tendencies. It agrees with nominalism for instance, in always appealing to particulars; with utilitarianism in emphasizing practical aspects; with positivism in its disdain for verbal solutions, useless questions, and metaphysical abstractions.